The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introductio...The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.展开更多
The charge-doping effect on the geometric and the electronic structures of organosilicon oligomers nSix(C=C)+y has been studied using density functional theory. Charge-doping can significantly lower the excitation ene...The charge-doping effect on the geometric and the electronic structures of organosilicon oligomers nSix(C=C)+y has been studied using density functional theory. Charge-doping can significantly lower the excitation energies. Interchain hole hopping mainly occurs between the π-conjugated units. A doped nSix(C=C)+y oligomer can undergo a structural rearrangement. The simulated UV/vis absorption peak of the rearranged structure is located at higher energy than the non-rearranged one. The hole transfer rate is significantly decreased if a doped molecule undergoes a rearrangement. These results offer a basis to explain previously observed experimental phenomena.展开更多
This is an introduction to antilinear operators. In following Wigner the terminus antilinear is used as it is standard in Physics.Mathematicians prefer to say conjugate linear. By restricting to finite-dimensional com...This is an introduction to antilinear operators. In following Wigner the terminus antilinear is used as it is standard in Physics.Mathematicians prefer to say conjugate linear. By restricting to finite-dimensional complex-linear spaces, the exposition becomes elementary in the functional analytic sense. Nevertheless it shows the amazing differences to the linear case. Basics of antilinearity is explained in sects. 2, 3, 4, 7 and in sect. 1.2: Spectrum, canonical Hermitian form, antilinear rank one and two operators,the Hermitian adjoint, classification of antilinear normal operators,(skew) conjugations, involutions, and acq-lines, the antilinear counterparts of 1-parameter operator groups. Applications include the representation of the Lagrangian Grassmannian by conjugations, its covering by acq-lines. As well as results on equivalence relations. After remembering elementary Tomita-Takesaki theory, antilinear maps, associated to a vector of a two-partite quantum system, are defined. By allowing to write modular objects as twisted products of pairs of them, they open some new ways to express EPR and teleportation tasks. The appendix presents a look onto the rich structure of antilinear operator spaces.展开更多
The rational design and construction of novel two-dimensional(2D)carbon nitrides(CNs)beyond g-C_(3)N_(4) is a hot topic in the fields of chemistry and materials.Inspired by the polymerisation of urea,we have prepared ...The rational design and construction of novel two-dimensional(2D)carbon nitrides(CNs)beyond g-C_(3)N_(4) is a hot topic in the fields of chemistry and materials.Inspired by the polymerisation of urea,we have prepared a series of novel C-C bridged heptazine CNs UO_(x)(where x is the ratio of urea to oxamide,x=1,1.5,2,2.5,and 3),which are similar to(C_(6)N_(7))n,upon the introduction of oxamide.As predicted using density functional theory(DFT)calculations,the conjugated structure of UO_(x) was effectively extended from an individual heptazine to the entire material.Consequently,its bandgap was reduced to 2.05 eV,and its absorption band edge was significantly extended to 600 nm.Furthermore,its carrier transfer and separation were significantly enhanced,establishing its superior photocatalytic activity.The optimised UO_(2) exhibits a superior photocatalytic hydrogen production rate about 108.59 lmol h^(-1)(using 10 mg of catalyst)with an apparent quantum efficiency(AQE)of 36.12%and 0.33%at 420 and 600 nm,respectively,which is one of the most active novel CNs reported to date.Moreover,UO_(2) exhibits excellent photocatalytic activity toward the oxidation of diphenylhydrazine to azobenzene with conversion and selectivity reaching~100%,which represents a promising highly efficient 2D CN material.Regarding phenols degradation,UO_(2) also displayed significantly higher activity and durability during the degradation of phenol when compared to traditional g-C_(3)N_(4),highlighting its significant potential for application in energy,environment and photocatalytic organic reactions.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10871016)
文摘The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.
基金supported by the National Natural Science Foundation of China (51073048)the Science Foundation for Leading Experts in Academy of Harbin City of China (2010RFJGG016)+1 种基金the Science Foundation of Heilongjiang Postdoctoral Grant of China (LBHQ07058)the Science Foundation for Elitists of Harbin University of Science and Technology
文摘The charge-doping effect on the geometric and the electronic structures of organosilicon oligomers nSix(C=C)+y has been studied using density functional theory. Charge-doping can significantly lower the excitation energies. Interchain hole hopping mainly occurs between the π-conjugated units. A doped nSix(C=C)+y oligomer can undergo a structural rearrangement. The simulated UV/vis absorption peak of the rearranged structure is located at higher energy than the non-rearranged one. The hole transfer rate is significantly decreased if a doped molecule undergoes a rearrangement. These results offer a basis to explain previously observed experimental phenomena.
文摘This is an introduction to antilinear operators. In following Wigner the terminus antilinear is used as it is standard in Physics.Mathematicians prefer to say conjugate linear. By restricting to finite-dimensional complex-linear spaces, the exposition becomes elementary in the functional analytic sense. Nevertheless it shows the amazing differences to the linear case. Basics of antilinearity is explained in sects. 2, 3, 4, 7 and in sect. 1.2: Spectrum, canonical Hermitian form, antilinear rank one and two operators,the Hermitian adjoint, classification of antilinear normal operators,(skew) conjugations, involutions, and acq-lines, the antilinear counterparts of 1-parameter operator groups. Applications include the representation of the Lagrangian Grassmannian by conjugations, its covering by acq-lines. As well as results on equivalence relations. After remembering elementary Tomita-Takesaki theory, antilinear maps, associated to a vector of a two-partite quantum system, are defined. By allowing to write modular objects as twisted products of pairs of them, they open some new ways to express EPR and teleportation tasks. The appendix presents a look onto the rich structure of antilinear operator spaces.
基金supported by the National Key R&D Program of China (2020YFA0406101)the National Natural Science Foundation of China (21771033 and 22071020)+4 种基金the Fundamental Research Funds for the Central Universities (2412018BJ001 and 2412018ZD007)the “Hong Kong Scholar” Programme (XJ2018021)the General Research FundResearch Grants Council of Hong Kong SAR Government (18301117)Dean’s Research Fund [04425], Ed UHK。
文摘The rational design and construction of novel two-dimensional(2D)carbon nitrides(CNs)beyond g-C_(3)N_(4) is a hot topic in the fields of chemistry and materials.Inspired by the polymerisation of urea,we have prepared a series of novel C-C bridged heptazine CNs UO_(x)(where x is the ratio of urea to oxamide,x=1,1.5,2,2.5,and 3),which are similar to(C_(6)N_(7))n,upon the introduction of oxamide.As predicted using density functional theory(DFT)calculations,the conjugated structure of UO_(x) was effectively extended from an individual heptazine to the entire material.Consequently,its bandgap was reduced to 2.05 eV,and its absorption band edge was significantly extended to 600 nm.Furthermore,its carrier transfer and separation were significantly enhanced,establishing its superior photocatalytic activity.The optimised UO_(2) exhibits a superior photocatalytic hydrogen production rate about 108.59 lmol h^(-1)(using 10 mg of catalyst)with an apparent quantum efficiency(AQE)of 36.12%and 0.33%at 420 and 600 nm,respectively,which is one of the most active novel CNs reported to date.Moreover,UO_(2) exhibits excellent photocatalytic activity toward the oxidation of diphenylhydrazine to azobenzene with conversion and selectivity reaching~100%,which represents a promising highly efficient 2D CN material.Regarding phenols degradation,UO_(2) also displayed significantly higher activity and durability during the degradation of phenol when compared to traditional g-C_(3)N_(4),highlighting its significant potential for application in energy,environment and photocatalytic organic reactions.
